Local and Global Stability Analysis of a Mathematical Model of Measles Incorporating Maternally-Derived-Immunity

Abstract

In this paper, the local stabilities of both the Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) were analyzed using the Jacobian matrix stability technique. The global stabilities were analyzed using Lyapunov function. The analysis shows that the DFE is locally and globally stable if the basic reproduction number R 0  1 R 0  1 and R 0  1 respectively. The EE is also locally and globally stable if . Vaccination and recovery rates have been shown from the graphical presentation as the important parameter that will eradicate measles from the population.